Expense constrained bidder optimization in repeated auctions Ramki Gummadi Stanford University (Based on joint work with P. Key and A. Proutiere)

Overview Introduction/Motivation Budgeted Second Price Auctions A General Online Budgeting Framework Optimal Bids for Micro-Value Auctions Conclusion

Three Aspects of Sponsored Search 1.Sequential setting. 2. Micro-transactions per auction. 3. The long tail of advertisers is expense constrained.

Motivation: Expense Constraints Payments are explicit, but valuations are abstract. Significantly alters bidding behavior. Critical for advertisers in the long tail.

Modeling Expense Constraints Balance time T0 B

Modeling Expense Constraints Stochastic fluctuations could cause spend rate different from target. Balance time T0 B

Modeling Expense Constraints “…the nature of what this budget limit means for the bidders themselves is somewhat of a mystery. There seems to be some risk control element to it, some purely administrative element to it, some bounded- rationality element to it, and more…” -- “Theory research at google”, SIGACT News, 2008.

Modeling Expense Constraints Balance time 0 B

Responsibility for expense constraints Auctioneer Bidder Bids fixed -- Auction entry throttled. Bids adjusted dynamically. Online bipartite matching between queries and bidders. Online knapsack type problems. Expense constraints = fixed budget. Possible to model more general expense constraints.

Bid optimization

Modeling aspects Expense constraints include a running balance constraint together with a fixed income per time slot. Random i.i.d. environment models aggregate statistics. -- observable and non-observable components. Bids are lower because any money saved can instead be used to buy a cheaper auction in the future. Objective function is infinite horizon expected utility, but with a discount factor that models limited patience.

Preview

Preview: Optimal Shading factors

Overview Introduction Budgeted Second Price auctions A General Online Budgeting Framework Optimal Bids for Micro-Value Auctions Conclusion

Model: Budgeted Second Price

The Value Function

But boundary conditions can not be inferred from the DP argument. Current auction Loss Win

Future opportunity cost Characterization of value function

Value Iteration:

Limiting case: micro-value auctions

Overview Introduction Budgeted Second Price Auctions A General Online Budgeting Framework Optimal Bids for Micro-Value Auctions Conclusion

General Online Budgeting Model Decision Maker Unobservable

Ex1: Second Price Auction

Ex2: GSP Auction Click events for L slots

Overview Introduction Budgeted Second Price Auctions A General Online Budgeting Framework Optimal Bids for Micro-Value Auctions Conclusion

Notation:

Theorem

Application to Second Price Auctions

Second Price Auction Example Opponents bid p Value functions

Optimal bid i.e., Static SP with shaded valuation:

Optimal Scaling factor

Optimal Bid: GSP Static GSP with “virtual valuation”:

Proof Overview Next 2 slides

time B(t) B Play U*

Overview Introduction MDP for budgeted SP auctions A General Online Budgeting Framework Optimal Bids for Micro-Value Auctions Conclusion

Stationarity in large markets

Conclusion A two parameter model for expense constraints in online budgeting problems. Optimal bid can be mapped to static auction with a shaded virtual valuation. Paper has more contents: MFE analysis and a finite horizon model.